How to Use Area Models to Multiply One-Digit Numbers By Two-digit Numbers

An area model multiplies a one-digit number by a two-digit number by splitting the two-digit number into tens and ones, multiplying each part separately, and adding the two areas. Below: how to draw and label the rectangle, and worked examples.

A Step-by-step Guide to Using Area Models to Multiply One-Digit Numbers By Two-digit Numbers

Using area models to multiply one-digit numbers by two-digit numbers can help students visualize the multiplication process. Here’s a step-by-step guide using the example \(5 x 12\).

Step 1: Draw the Area Model

Start by drawing a large rectangle. This rectangle will represent the entire multiplication problem.

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Step 2: Divide the Rectangle

Next, divide the rectangle into two parts. This is because we’re multiplying by a two-digit number (12). The larger part represents the tens place (10), and the smaller part represents the ones place (2). Label each section.

It would look something like this:

-----------------
| 10 | 2 |
-----------------

Step 3: Write the One-Digit Number

On the side of the rectangle, write the one-digit number you’re multiplying (5).

 -----------------
5 | 10 | 2 | -----------------

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Step 4: Calculate the Area

The area of a rectangle is found by multiplying its length by its width. So, multiply the one-digit number (5) by each part of the two-digit number (10 and 2).

For the first part of the rectangle: \(5 x 10 = 50\)
For the second part of the rectangle: \(5 x 2 = 10\)

Write these products inside the respective parts of the rectangle.

 -----------------
5 | 50 | 10 | -----------------

Step 5: Add the Areas

Finally, add the two areas together. In this case, \(50 + 10 = 60\).
So, \(5 x 12 = 60\).
Area models are a great way for students to visualize multiplication, breaking down complex problems into simpler, more manageable parts. It’s especially useful for students who are visual learners.

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More Area Model Examples: 2-Digit Times 1-Digit

Example 1: 7 × 36

Split 36 into 30 and 6. Each box holds one partial product.

Add the boxes: 210 + 42 = 252. So 7 × 36 = 252.

Example 2: 4 × 58

Add: 200 + 32 = 232. So 4 × 58 = 232.

Tip: To multiply 4 × 50, think 4 × 5 = 20, then attach the zero to get 200. You can also split a number another way and get the same answer. For 7 × 36, try 7 × 20 = 140 and 7 × 16 = 112. Then 140 + 112 = 252. Tens and ones is usually the easiest split.

Try It: Area Model Multiplication Problems

Draw an area model for each one, then check your answer.

1. 6 × 24
2. 3 × 47
3. 8 × 53
4. 9 × 75

Answers:

1. 6 × 20 = 120 and 6 × 4 = 24, so 120 + 24 = 144
2. 3 × 40 = 120 and 3 × 7 = 21, so 120 + 21 = 141
3. 8 × 50 = 400 and 8 × 3 = 24, so 400 + 24 = 424
4. 9 × 70 = 630 and 9 × 5 = 45, so 630 + 45 = 675

Frequently Asked Questions

How do you use an area model for 2-digit by 1-digit multiplication?

Break the 2-digit number into tens and ones, write those parts across the top of a rectangle, and put the 1-digit number on the side. Multiply in each box, then add. For 4 × 58, the boxes are 4 × 50 = 200 and 4 × 8 = 32, so 4 × 58 = 232. Saying the partial products aloud helps students avoid adding the digits incorrectly.

How do you draw an area model?

Draw one long rectangle and split it with a vertical line into a bigger section for the tens and a smaller section for the ones. Label the top with the parts, such as 60 and 3 for 63, and write the single-digit factor, such as 5, along the left side. Then fill each section with its product, 300 and 15, and add them to get 315.

How do you use an area model divided into two regions?

Each region holds one partial product. For 6 × 23, the left region is 6 by 20 and the right region is 6 by 3. Their areas are 120 and 18. Add the two regions to find the whole rectangle: 120 + 18 = 138. So 6 × 23 = 138, which matches 6 × (20 + 3).

How do you use an area model for 2-digit by 2-digit multiplication?

Split both numbers into tens and ones, which makes four boxes. For 34 × 26, write 30 and 4 across the top and 20 and 6 down the side. The boxes are 600, 80, 180 and 24. Adding them gives 600 + 80 + 180 + 24 = 884. Once students are comfortable with the two-box version, this grid is a natural next step.

What is an open area model in multiplication?

An open area model is a rectangle sketched without grid squares or exact sizes. It only needs to show the parts and their labels, so it is quick to draw for larger numbers. For 8 × 47, sketch a rectangle split into 40 and 7, write 8 on the side, and fill in 320 and 56. The total is 376.

How do you use an area model for 2-digit by 1-digit division?

Treat the dividend as the area and the divisor as one side, then find the missing side in friendly chunks. For 96 ÷ 4, take out 80 first, since 4 × 20 = 80, which leaves 16, and 4 × 4 = 16. The missing side is 20 + 4 = 24, so 96 ÷ 4 = 24. Multiplying 4 × 24 confirms it.